Response-Aware Coarse-Graining in Summary-Mediated Opinion Dynamics
Abstract
Interacting populations increasingly respond to compressed representations generated from their own collective state. We ask which information such an endogenous coarse-graining must preserve in order to reproduce the collective dynamics. The question has two complementary answers for continuous opinions with attraction, indifference, and repulsion. Inside any strict K-bloc response cell where every represented stance attracts every bloc, the dynamics reduce exactly to translation and disagreement. The represented distribution's shape cancels from all disagreement modes, which form a homogeneously anchored weighted signed-Laplacian system, while represented-mean error acts only on translation. This reduction yields a geometry-dependent stability boundary and shows that prevalence bias produces secular drift at marginal stability only through its projection onto the neutral eigenspace. Outside that common linear-response regime, threshold geometry makes distributional information observable. The induced force discrepancy is a behavior-defined integral probability metric; restricted force probes identify generic finite empirical discussions, and for finitely supported candidates uniform force error controls total-variation and Wasserstein error while support reduction incurs a nonzero distortion floor. A cumulative-discrepancy characterization further explains why transport-small summaries can remain behaviorally inaccurate at response thresholds. Mode-resolved integrations, projected particle simulations, finite-size ensembles, and threshold-crossing experiments test these two regimes. As a deployment consequence, broadcast summary error survives as collective noise whereas independently personalized error self-averages. The model is stylized and not empirically calibrated; generated discussion summaries motivate the general problem of endogenous, response-aware coarse-graining.
Related
- Coarse-Graining and Long-Range Response in Generated Systems
- Coarse-graining far-from-equilibrium dynamics using oblique projectors
- Dynamics-structure interchangeability in binary opinion models on multiplex networks
- Nonlinear Opinion Dynamics of Stubborn Individuals in Time-Varying Cooperation–Competition Networks
- Inferring the microscopic mechanisms of opinion dynamics using a kinetic Ising model
BibTeX
@misc{araujo2026responseaware,
title = {{Response-Aware Coarse-Graining in Summary-Mediated Opinion Dynamics}},
author = {Ruben E. Araújo},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.05560},
eprint = {2609.05560},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.05560},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Response-Aware Coarse-Graining in Summary-Mediated Opinion Dynamics
AU - Ruben E. Araújo
PY - 2026
DA - 2026/09/03
PB - arXiv
DO - 10.48550/arxiv.2609.05560
UR - https://arxiv.org/abs/2609.05560
AB - Interacting populations increasingly respond to compressed representations generated from their own collective state. We ask which information such an endogenous coarse-graining must preserve in order to reproduce the collective dynamics. The question has two complementary answers for continuous opinions with attraction, indifference, and repulsion. Inside any strict K-bloc response cell where every represented stance attracts every bloc, the dynamics reduce exactly to translation and disagreement. The represented distribution's shape cancels from all disagreement modes, which form a homogeneously anchored weighted signed-Laplacian system, while represented-mean error acts only on translation. This reduction yields a geometry-dependent stability boundary and shows that prevalence bias produces secular drift at marginal stability only through its projection onto the neutral eigenspace. Outside that common linear-response regime, threshold geometry makes distributional information observable. The induced force discrepancy is a behavior-defined integral probability metric; restricted force probes identify generic finite empirical discussions, and for finitely supported candidates uniform force error controls total-variation and Wasserstein error while support reduction incurs a nonzero distortion floor. A cumulative-discrepancy characterization further explains why transport-small summaries can remain behaviorally inaccurate at response thresholds. Mode-resolved integrations, projected particle simulations, finite-size ensembles, and threshold-crossing experiments test these two regimes. As a deployment consequence, broadcast summary error survives as collective noise whereas independently personalized error self-averages. The model is stylized and not empirically calibrated; generated discussion summaries motivate the general problem of endogenous, response-aware coarse-graining.
ER -